User Guide

Sound System Design Reference Manual
Acoustical Feedback and Potential
System Gain
Just as in the outdoor case studied earlier,
if we have a microphone/amplifier/loudspeaker
combination in the same room and gradually turn up
the gain of the amplifier to a point approaching
sustained feedback, the electrical frequency
response of the system changes with the gain
setting. The effect results from an acoustic feedback
path between the loudspeaker and the microphone.
As a person talks into the microphone, the
microphone hears not only the direct sound from the
talker, but the reverberant field produced by the
loudspeaker as well.
The purpose of using high-quality loudspeakers
and microphones having smooth response
characteristics, and sound system equalization (apart
from achieving the desired tonal response) is to
smooth out all of the potential feedback points so
that they are evenly distributed across the audible
frequency range. When this has been done, there
should be as many negative feedback points as
positive feedback points, and the positive feedback
points should all reach the level of instability at about
the same system gain.
We might expect this to average out in such a
way that the level produced by the loudspeaker
reaching the microphone can never be greater than
that produced by the talker without causing sustained
oscillation. In other words, we assume that the extra
gain supplied by all the positive feedback spikes is
just balanced out by the loss caused by all the
negative feedback dips.
If the Boner criteria for optimum system
geometry are followed, the microphone will be close
to the talker so that it hears mostly direct sound from
the talker. It will be far enough from the loudspeaker
to be well into the reverberant field of the
loudspeaker, so that direct sound from the
loudspeaker is not an appreciable factor in triggering
system feedback. Assuming that listeners are also in
the reverberant field of the loudspeaker, it follows
that the sound level in the listening area with the
system turned on cannot be greater than that of the
unaided talker at the microphone position with the
system turned off. Using the Boner concept of
system delta , the situation at maximum gain
corresponds to a delta of unity. (Delta is defined as
the difference in decibels between sound level at the
system microphone with system off and the level in
the audience area with system on. See Figure 6-1).
Although we have described these as
conditions of maximum potential system gain, it is
possible in practice to achieve a delta greater than
unity. For example, if a directional microphone is
used it can discriminate against the reverberant field
and allow another 3 to 4 dB of system gain. Another
possibility is to place the listener in the direct field of
the loudspeaker, allowing a further increase in
system gain. If the level of the reverberant field is
lower in the performing area than in the listening
area, additional system gain also results. This
situation is described by the Boners as a room
constant in the microphone area different from that in
the seating area. Similar results may be noted in
rooms having large floor areas, relatively low
ceilings, and substantial sound absorption. In such
rooms, as we have seen, sound from a point source
tends to dwindle off beyond D
C
at a rate of 2 or 3 dB
for each doubling of distance rather than remaining
constant in level.
Still another way to increase gain is to
electrically suppress the positive feedback
frequencies individually with very narrow bandwidth
filters. If one could channel all energy into the
negative feedback frequencies, the potential system
gain would theoretically become infinite! Unfortunately,
the acoustic feedback path is not stable enough to
permit this degree of narrow-band equalization.
In all other situations, a gain setting is reached
at which sustained oscillation occurs. By definition,
maximum system gain is reached just below this
point. However, the system cannot be operated
satisfactorily at a point just below oscillation because
of its unpleasant comb-filter response and the
prolonged ringing caused by positive feedback
peaks. To get back to reasonably flat electrical
response and freedom from audible ringing, it usually
is recommended that a properly equalized system be
operated about 6 dB below its maximum gain point.
Even an elaborately tuned system using narrow-
band filters can seldom be operated at gains greater
than 3 dB below sustained oscillation.
Sound Field Calculations for a Small Room
Consider the room shown in Figure 6-2. This is
a typical small meeting room or classroom having a
volume less than 80 m
3
. The average absorption
coefficient α is 0.2. Total surface area is 111 m
2
. The
room constant, therefore, is 28 m
2
.
From the previous chapter, we know how to
calculate the critical distance for a person talking
(nominal directivity index of 3 dB). In the example
given, D
C
for a source having a directivity index of 3
dB is 1 meter.
The figure also shows geometrical relationships
among a talker, a listener, the talker’s microphone
and a simple wall-mounted loudspeaker having a
directivity index of 6 dB along the axis pointed at the
listener. The microphone is assumed to be
omnidirectional.
6-2